Test Coils Data
The
resistance of each coil was determined by passing a known current through the
coil and measuring the voltage drop across the terminals of the coil. Three different
current settings were used and the average resistance determined. As a comparison
the resistance was also calculated from the coil parameters using the coil
resistance equation as derived in the theory section. The inductance of each
coil was also determined by direct measurement using a multimeter (method 1) and
also by the inductance measuring
method described in the theory section (method 2). The number of turns in
each coil is a calculated quantity with the exception of the sensor coils which
were counted (I was too lazy to count the turns as I wound the coils). Coils C
and D show a notable difference between the inductance values obtained using the
two methods, it's not entirely clear why this is the case but it can be accounted
for in part by the inherent error of the multimeter measurements at low values.
The inductance values are also determined by calculation using the inductance
formula which can be found in the theory section. There is a significant difference
between the measured and calculated values for the drive coils. As mentioned earlier,
N is an estimated value based on the dimensions of the windings and since the
result depends on N^{2} this is the most likely source of the discrepancy.
The calculated result is in much better agreement when the number of turns is
accurately known, as in the case of the sensor coil.
The treatment of
errors is not 100% rigorous, I've put them in to remind myself they exist! The
firm adherence to significant figures is also a bit ropey. I'll tighten this up
later.
Something which
is worth noting is that the coil time constants vary much less than the inductance
values which range over more than an order of magnitude.
The coil data are
tabulated below:
Coil A 



Voltage (V) 
2.6 +/ 0.05

5.3 +/ 0.05

8.5 +/0.05

Current (A) 
2.0 +/ 0.05

4.0 +/ 0.05

6.0 +/ 0.05

Resistance () 
1.30 +/ 0.04

1.325 +/ 0.025

1.417 +/ 0.020

Average Resistance () 
1.35 +/ 0.03



Calculated Resistance () 
1.40



Number of Turns 
480



Outer Radius (mm) 
19.4



Inner Radius (mm) 
7



Length (mm) 
25.7



Wire Diameter (mm) 
0.8



Inductance (mH) method 1 
2.04



Inductance (mH) method 2 
1.98



Calculated Inductance (mH) 
2.91



Time Constant (ms) 
1.49



Coil B 



Voltage (V) 
1.1 +/ 0.05

2.2 +/ 0.05

3.3 +/ 0.05

Current (A) 
2.0 +/ 0.05

4.0 +/ 0.05

6.0 +/ 0.05

Resistance () 
0.55 +/ 0.04

0.55 +/ 0.02

0.550 +/ 0.013

Average Resistance () 
0.55 +/ 0.02



Calculated Resistance () 
0.52



Number of Turns 
300



Outer Radius (mm) 
18.5



Inner Radius (mm) 
7



Length (mm) 
26.3



Wire Diameter (mm) 
1.0



Inductance (mH) method 1 
0.798



Inductance (mH) method 2 
0.763



Calculated Inductance (mH) 
1.08



Time Constant (ms) 
1.39



Coil C 



Voltage (V) 
0.49 +/ 0.005

0.97 +/ 0.005

1.4 +/ 0.05

Current (A) 
2.0 +/ 0.05

4.0 +/ 0.05

6.0 +/ 0.05

Resistance () 
0.245 +/ 0.009

0.243 +/ 0.004

0.233 +/ 0.011

Average Resistance () 
0.24 +/ 0.01



Calculated Resistance () 
0.23



Number of Turns 
180



Outer Radius (mm) 
18.9



Inner Radius (mm) 
7



Length (mm) 
26.7



Wire Diameter (mm) 
1.25



Inductance (mH) method 1 
0.316



Inductance (mH) method 2 
0.253



Calculated Inductance (mH) 
0.392



Time Constant (ms) 
1.05



Coil D 



Voltage (V) 
0.28 +/ 0.005

0.56 +/ 0.005

0.82 +/ 0.005

Current (A) 
2.0 +/ 0.05

4.0 +/ 0.05

6.0 +/ 0.05

Resistance () 
0.140 +/ 0.006

0.140 +/ 0.003

0.137 +/ 0.002

Average Resistance () 
0.14 +/ 0.04



Calculated Resistance () 
0.11



Number of Turns 
130



Outer Radius (mm) 
18.3



Inner Radius (mm) 
7



Length (mm) 
27.5



Wire Diameter (mm) 
1.5



Inductance (mH) method 1 
0.167



Inductance (mH) method 2 
0.099



Calculated Inductance (mH) 
0.195



Time Constant (ms) 
0.707



Sensor Coil 

Resistance () 
48.4 +/ 0.05

Calculated Resistance () 
44.5

Number of Turns 
500

Outer Radius (mm) 
24.5

Inner Radius (mm) 
22

Length (mm) 
9

Wire Diameter (mm) 
0.2

Inductance (mH) method 1 
18.08

Inductance (mH) method 2 

Calculated Inductance (mH) 
17.34

2 Stage Coilgun  Drive Coil 1 



Voltage (V) 
0.84 +/ 0.005

1.72 +/ 0.005

2.60 +/ 0.005

Current (A) 
2.0 +/ 0.05

4.0 +/ 0.05

6.0 +/ 0.05

Resistance () 
0.42

0.43

0.43

Average Resistance () 
0.43



Calculated Resistance () 
0.41



Number of Turns 
240



Outer Radius (mm) 
17.2



Inner Radius (mm) 
7.5



Length (mm) 
25.4



Wire Diameter (mm) 
1.0



Inductance (mH) method 1 
0.522



Inductance (mH) method 2 
0.444



Calculated Inductance (mH) 
0.692



Time Constant (ms) 
0.97



2 Stage Coilgun  Sensor Coil 1 

Resistance () 
11.1 +/ 0.05

Calculated Resistance () 
12.8

Number of Turns 
150

Outer Radius (mm) 
18.5

Inner Radius (mm) 
17.2

Length (mm) 
6.5

Wire Diameter (mm) 
0.2

Inductance (mH) method 1 
1.01

Inductance (mH) method 2 

2 Stage Coilgun  Drive Coil 2 



Voltage (V) 
0.83 +/ 0.005

1.65 +/ 0.005

2.49 +/ 0.005

Current (A) 
2.0 +/ 0.05

4.0 +/ 0.05

6.0 +/ 0.05

Resistance () 
0.42

0.41

0.42

Average Resistance () 
0.42



Calculated Resistance () 
0.41



Number of Turns 
240



Outer Radius (mm) 
17.0



Inner Radius (mm) 
7.5



Length (mm) 
26.1



Wire Diameter (mm) 
1.0



Inductance (mH) method 1 
0.538



Inductance (mH) method 2 
0.453



Calculated Inductance (mH) 
0.675



Time Constant (ms) 
1.02



2 Stage Coilgun  Sensor Coil 2 

Resistance () 
11.0 +/ 0.05

Calculated Resistance () 
14.0

Number of Turns 
150

Outer Radius (mm) 
18.5

Inner Radius (mm) 
17.0

Length (mm) 
6.2

Wire Diameter (mm) 
0.2

Inductance (mH) method 1 
1.05

Inductance (mH) method 2 

